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D 5 6 C-7
Large Eddy Simulation of flow around a Horizontal-axis wind Turbine at Different
Rotational Speed
A. A. Veisi
Department of Mechanical Engineering Sistan and Baluchestan University, Zahedan, Iran
M. H.ShafieiMayam
Department of Mechanical Engineering,Bozorgmehr-University of Qaenat, Qaen, Iran
Abstract
The present study focuses on the flow around a horizontal axis wind turbine. Large Eddy Simulation has been employed in order to
study the flow at different rotational speeds. Anisotropic residual stress tensor is driven by The Smagorinsky model. Three
simulations were performed at different tip speed ratio of 3, 6 and 10. The acquired results are in good agreement with presented
experimental data in literatures. It is also revealed that development of the wake is decreased when downstream velocity is increased
along the horizontal line at different downstream distance of wind turbine. In addition, velocity defect behind the wind turbine is
increased when tip speed ratio increases but the recovery of wake is happened faster. At rotational speed equals 6, minimum velocity
is 54% of the initial velocity and maximum efficiency is 67% at the lateral section of wind tunnel where the tip of blade is located,
while they are 26% and 68% respectively when rotational speed is 10. Turbulence intensity is increased by increasing Tip Speed
Ratio while separated vortices from the blade are disappeared later. The effect of separated vortices from the blades of wind turbine
are not seen when rotational speed is 3, while they are revealed at rotational speed of 6 and 10. As a result, it can be concluded that
the effect of separated vortices are augmented when rotational speed is increased.
Keywords :Wind turbine, large eddy simulation, turbulence flow, Smagorinsky subgrid-scale model.
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Wake
Turbulence Intensity
2
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shafiei@buqaen.ac.ir :
95/02/01 :
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95/06/01 :( ) !
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4
Reynolds-Averaged-Navier-Stokes (RANS)
5
Reynolds Stress Models
Large Eddy Simulation (LES)
Near wake
3
Far wake
2
340
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Mixed models
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Closure problem
Mixing-length hypothesis
341
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= Z 3 5 MF = F . 4 TI =%0/3 5 MF = F
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4
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c[ = 7
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Sliding mesh technique
342
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3 > 3 Y4
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F3
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3
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8
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/- 3. 4 F
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L4
+ 3
+ E M ‚ ? L ^B D
8 wOL 4 ^0
> . 3
Q/ + K@t X3 9 B 3
@
cd L 4
S 0 F C + / 3 8 B O3
+ E L 4 Q/
F , 5 MF + / V 4 5 = L 3 . F 3 . C
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8 X - +E 3>3
@
3 3
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,
0
3
S
@
+ - 3 +d
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F
3. C
: + 3 F
/B. :/ . 4
3
0 ] F ,
4>
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+/ L 4
3 3X zL
L 4 ^ 0 ^9
. F
3 03 3 > 3
.
X . F V
:4
0 F C + / 3 8 = c λ1=3
F - = c >
S
L4
:
JD 6 YD λ1=3 + 3 ^9
λ=6 10 + 3
(Z/R=1)
S
@
2Z
S
L4
Q; 3
. F3
9>3
` @ λ2 = 6
/
-
2
3
343
VW = 0/26
7D
L4
1D XZ
Blockage ratio
Turbulent mixing
L4
5/ ( ?P Q 7/ 7 *) 1 V4
- / '()
4 + -4 N
* / * 0 * .1 ' /
@
C
:
JD
(Z/R=1) 2Z
` @ λ 3 =10
@
3 03 ` @
/ 1D $ , / +,- MZ /-
4 + -3 N
X3 9 u ? 3
= 9 7C 3
S
c 5 = L 3 .
8 9
+ E 3 F 7C X3 9 = c . C
5 MF
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S
L4
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6 + /X F) F
3>3 0 ] L 4.
F
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3
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+ / L 4 R @> 3 .(8
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[20] *) 1 V4
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3
VW = 0/54
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4 + -5 N
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3 7 [20] > / (5 4) + /X F
F
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3 > 3 + / +0 4R
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B 3. C.
[20] > / +0 4 F . 4 . 2 23
1
q;
F 0 5 = L 3 . 4 F X@
+ 3 a b =1
0 I J >
4E
F I > 0 . 4 F X@ t
1
Viscous sublayer
343
3 >3
4>
λ1 = 3
=
r
-3
+/ L 4 3 = M
.
4
. D -2-4
4 3
K
3
L 4 +/
3 +d 0 -O3 3 > 3 . 4
8 9 IJ
λ2=6
Q/ . C + 4
L 4 5 = L 3.
v)C
p
+ D3 4 3 . 3
Q ; + :L
?L + 4
> 3 QV 1 7C AtV
3>3
4>
+ 0
L4
0 F + 8Y4 + /
9X F. V1
3
3
0]
0
F + 8Y4
λ1=3 + 3 3 X
+
L 4X
D -6 N
0 ] 1D
3>3
5) :M . '() N ,7)
4 + -7 N
e2=6 5-)* / * N .1 5/7 7 - ] 1D 7 / *
@
5) : M . '() N ,7)
4 + –8 N
e3 =10 5-)* / * N .1 5/7 7 - ] 1D 7 / * 0 * .1
wO- + 3
. DDE 0 + 3 0
+/
@ > 3 ; : 3 9 . 1 F 3 : m4
3 8 .
^9
. F 3 : I9 3 8 6 -V 1 + /
@ W2J F 3
wO- + 3 3 8 q O 4 ( 6 0 M 4
:/ i ? >
/( . /
./ 3 8 V4 .
R
.
. DDE Y4 / 3 8 .
wO- + 3 + 0 + /n 5
/ 3 8q O4
4 3 /( > > A I . 4 F 7 -
λ1 = 3
+ 3
^0 >
3. F
. 3
L4
X/D=0/62 X/D=- 0/62 0 λ2=6
Q;
L4Q; 3
QO 5 = L
3>3
- @
. C+ 4
L4
F
L4
L 4 . N2 O
+/ L 4
L4
λ1=3
4 -3(
+ 8 9 XE ) 3 > 3 ;
. C+ 4
L4 . 3
Q/
L4
+/
:4 3
@ 3
L 4>
F
/M
λ2 = 6
@ 3
4 -3
+/
8 9 XE
;
L4
= L 3. F
/- + : L 4
:4 3
3 . C 0 +d
F 3 .;
L4Q; 3 5
XE
;
L 4 Q/ > . 3
Q;
+/
: 9
C +/ 3 8
- B O3
> [:/ / S + 8 9
+ 3. C+ 5 > 4 >
:4 3
@ 3. F3 / 0 F
V
L 4 ^0
F „M@
L4
/
. F
/ * 0 * .1 -
-]
F
XZ
λ 2 =6 λ 1 =3
L4
+ 3 . C + 4
+ 8Y4
L 4 + / 3) /
Q : = M
4>
Q; 3
L4
/ .( 4 F ? . 3
0 F
Z/D=1 . 3
Q; . C+ 4
L4 4>
2Z
+ 3X/D= 0/52 X/D=- 0/52 XZ
. D
^0
M
0 * .1 - ]
A B . C +0 4
'()
3 >3
/ VW
3> 3
3 3 λ2 + 3
. F3
VW = 0/67
E
/
... + / L 4 3 D
=0/68 3 3 λ 3 + 3
-
5 6 *-/): -3-4
K 3 3>3
@
MF . C + / V 4 73 n7
+ /> 3
3 3 . C 0 XZ @
+/ 3 .
:
:/ 0 + 3 i ; @ B +0 4
73 > [:/
4>
3 +
8Q 3q @ i? > . 4
V3+ 3
n7 8o 6 .
@
MF + / V 4
^0
0 F C [
+/ 3 8 D E 3> 3 R @. C
4
344
>
10 X F)
@
6 . +C 3
. F
(v 10X F)
@
4
3-
M/ 3 3 λ 2 =6 + 3
wO- λ3 =10
L4
1 n/ 3 + / 3 8 0
@ 6
(N
/ 3 8W9
4
M4 (
3
3. F3
2f
L4.
8
4 3
∆ ([26]) g + / r
4 3
2E + / I
F
F C + / 3 8 10 X F . F 3 ([29]) gZ# ([28]) h ([27])
= M
+ / L 4 + KE L 4 .
3>3 0
F C +/ 3 8 I . /
. - gi ( 0 M 4 3
n
I M-
@ :E
I
4 4 3 3 λ1=3 + 3
(N )
(v)
"#$ / (' -
, O- [ *
5) :M . '() 5 6 -/)*)
4) 5
- / '()
5) :M . 5 6 . D -9 N
(b7/ . ) e2=6 (c) (I7- . )e1=3 (aP-) .(b. a4/ ) Z/D=7 7 (b7/ a4/ ) Z/D=4 (I7- a4/ ) Z/D=1 N$-., / X-Y
0
345
F C + / 3 8 = c λ1=3
0 F C+/ 3 8 F
L4
6 ;
. 3
@
Q;
7
Q; 3
0 F C +/ 3 8 ]
/
.- U >
L4Q; 3 5 = L 3. 3
Q;
L4
QV 1 = 9
@
3
Q/
, 3 8 > 3 2Z
345
3
5 V 0 F + / 3 + 3 + I . L 3 5 MF = F
11) + /X F . F
M 4 3 > 3 6 N2 O + /QO3
YV
N2 O XZ
5 MF = F
0 Y4 (13
F
. - N2 O
+/ L 4 + 3 3 X ;
D
- 3 8 = c λ3 =10
= c F
. F
-
. F
;
;
@
@ >
C +/ 3 8 3
L 4Q ; 3.
;
S 0
@
0 F C +/
F C+/ 3 8
... + / L 4 3 D
E
. 4
F
+ -3
0 F
0 F C+/ 3 8= c
A B . C +0 4
B
-4-4
3> 3
d # [9
(N )
(v)
(q)
e3 =10 (f) e2=6(c) e1=3 (aP-) a K
+ 3 L; 6
4>
3 + /> 3
@
n7
Z fV 6 . 4
- 7/ 5 6'()
mf K
V3+
/ 5- e"P '()
3 3> 3
3 :/ 0
-
/ / * 0 * .1 -
0 ] 5 MF = F 3
0 ] 5 MF = F I J
-
5 6 *-/): -10 N
3 X + 3
> 0. 4;1
5 MF = F
3 3>3
346
0 F C [
+/ 3 8 3 > 3 6 ;
4 F wO- . F
, > 3 + / QV 1 Y4
. F 3 / (0
;
n7 ^
/ 3 8
C + / 3 8 / . - 2E
- 3 € D (13 11) + /X F
€D > = c 4 >
2Z Q ; 3 F 3
0 F
U . F
-3
0 F C +/ 3 8 ,
-3
/ 3 8> = c l3
+/ L 4
/
.-
>
F3
n
I M-
@ :E
>
-]
5) :M .
d # [9
.
>3 0
0 F C + / 3 8 = c λ 1 =3
0 F C +/ 3 8 = c
8 , .
> 3 3. F :
+ 3. 3
Q ; 3 > 3 +/
L4Q; 3
L 4 (Z/R=1) 2Z
3X
? IIJD
R`
4 + -12 N
X9 @ λ3 =10
e2=6 5-)* / * N .1 5/7 7 - ] 1D 7 / * 0 * .1
D
` @
λ2 + 3 3 > 3
5 MF = F. F 3
S
-]
5) :M .
d # [9
e3 =10 5-)* / * N .1 5/7 7 - ] 1D 7 / * 0 * .1
-
. F3
TI=%11/01
5 MF = F
7D
1D XZ
@
TI=%19/98 3 3 λ3 + 3
P 3
4>
D
5 MF = F
TI=%14/62 3 3
2Z Q ; 3 -V 1 = 9
-5
- L 4 E D E 3>3 6 R @. C I J >
0 M 4 3 H ;3 + / 3 8 +0 4 F ( 3 = M
+/
. 4
8 9 IJ
4 3
8 :4
F 0R
+ L I J
/ 5- 0 U 3 3 V W3 J I J > U
->
L 4.
+
Fp, +/ 4 3.
> /
+ / L 4 Q ; + E L 4 Q/ 0
@ 3>3
4
. F3
C
.
4>
7C
3 > 3 0 > 8 2Z 3 C > 3
3. F
3 03
+/ L 4 :
>3
L4
S + 8 9 XE
L 4 : €D
L4Q;
-]
5) :M .
d # [9
4 + -11 N
e1=3 5-)* / * N .1 5/7 7 - ] 1D 7 / * 0 * .1
λ1=3 0 P 3 /
:
i? >
F ,
€D > = F
L4 Q; 3
4 • . F . F
€t V
5 MF = F Q ;
7C 3
8
-3 :
3 5 = L 3. F
^ 4
3 03y . C.
-3
+
2Z
L4 .
L4 Q;
L4.
: €D C . F
3 03 > 3
4>
S 0 F C+/ 3 8 = c BV 3
S XE
i 3 C 3. C.
+/
@ , ^9
. F3
1
347
@
5 MF = F X9 @ λ2=6
I B0 F i ? > . 3
Q ; λ3 =10
L 4+ 3
5 MF = F F MF . C
0 . 4 MF . C
@6
4 F , + /QV 1 = F - P 0 F
MF . C
1 . 3 Q ; 5 MF
R I
1
75 V
3 > [:/ . F I
3 At
I . 4
= F .;
8 wO- (13 11) + /X F 3 3
5
3 L4 1/ . 3
Q;
L 4 Q ; 3 5 MF
4 I B
= c A)@ B V 3
V
:4
. 4 /. C 5
I B
Q ; 5 MF = F
4 + -13 N
5) :
@ 0
4 TI=%6/12
Self-sustaining
347
/= 0/68
3 3
L 4 + /.
` @ 4 3 3
/ VW =0/26 3 3λ + 3
/ VW =0/54
L4
` @
L4Q; 3
1. 8
, i ? > F3
. 3
Q ; ; /. ]
F C+/ 3 8 I
Q; ;
L4 .
3 / 3 8 > c .;
7C > :/ 3
+/ L 4 > + 3 3 03 ` @
4
@ > . 3
λ2 + 3 /
VW = 0/67
3 3
.
: + r . 1 F 3 λ3+ 3 VW
.;
F C +/ 3 8 ]
I 1 8 5 = L 3
L 4.
3 03
9+ C c E
L 4.
3 F C +/ 3 8 ]
I
B0 .
1 c
. C.
5 MF = F . ^ B 3 . C .
€t V = F
U
5 MF = F 4 3 3 i ? > .
7C X3 9 c ;
. 3
Q ; 5 MF = F
/
. - ? @ I J 0 XZ @
3 S + 8 9 XE
2E
- 3€D +
5 MF = F
F
A B . C +0 4
L4+ 3
3> 3
λ2
3 8 XE QV 1
BV 3i ? >
E
. F 3 )8 c . C Y4 .
3
. F3 / 0 F C +/ 3 8 m
... + / L 4 3 D
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3 ^9
. F 3 λ1=3 0 P 3
+/ L 4 : 0
Q; > . C.
3 /. c
F C+/ 3 8 C
3
B0 .
C 3.
- 3€D ,
5 MF = F
- 3 8> = c F C+/ 3 8]
L 4Q ;
Q ; 3 7C > :/ 3 .
>30
>3
4>
/
X
Q ; (λ3 =100 P 3) 5 MF = F 4 >
> 3 0 2Z
+~
F C +/ 3 8 F X
3 5 = L 3 . 3
= F ,
L4 .
3 /. c > 3
4>
MF + /. C /
7C 3 i ? > . 3
Q ; 5 MF
.
/R I
- :/ 5 MF
.;
4
g -) -7
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348